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The first dedicated virtual compton scattering experiment at MAMI
I
ELSEVIER
_A Nuclear Physics A663&664 (2000) 389c-392c www.elsevier.nl/locatelnpe
The First Dedicated Virtual Compton Scattering Experiment at MAMI J. M. Friedrich", P. Bartsch", D. Baumann", J. Berthot" , P. Y. Bertin", V. Breton" , W. U. Boeglin", R. Bohma , N. d'Hose", T. Caprano" , S. Derber", N. Degrande", M. Ding" , M. O. Distler", J. E. Ducret", R. EdelhofP, 1. Ewalda , H. Fonvieille'' , J. Friedrich", R. Geiges", Th . Gousset", P. A. M. Ouichon" , H. HolvoetC , Ch. Hyde-Wright", P. Jennewein", M. Kahrau", S. Kerhoas", M. Korn", H. Kramer", K. W. Krygier", V. Kunde", B. Lannoy", D. Lhuillier", A. Liesenfeld", C. Marchand", D. Marchand", J. Martino", H. Merkel", K. Merle", P. Merle", G. De Meyer", J. Mougey", R. Neuhausen", E. Offermann", Th. Pospischil", G. Quemener", O. Raveld , Y. Roblin", J. Roche", D. Rohe", G. Rosner", D. Ryckbosch", P. Sauer", H. Schmieden", S. Schardt" , G. Tamas", M. Tytgat" , M. Vanderhaeghen" , L. Van Hoorebeke", R. Van de VyverC , J. Van de Wielef , P. Vernia", A. Wagner", Th . Walcher" "Inst itut fur Kernphysik, Universitat Mainz, Germany bDAPNIAjSPhN, CEAjSaclay, F91191 Gif-sur-Yvette Cedex, France cUniversity of Gent , Belgium dLPC, Universite Blaise Pascal, IN2P3jCNRS Aubiere, France "Old Dominion University, Virginia, USA fIPN , IN2P3 Orsay, France We measured the absolute cross sections for photon electro-production off the prot on, ep ~ en, with the high resolution spectrometers at MAMI at momentum transfer q = 600 MeVjc and photon polarization (': = 0.62. We covered the momentum range for the outgoing real photon q' = 33-:-111 MeVjc. From the extr acted Virtual Compton Scattering amplitude we deduce values for two structure functions related to the generalized polarizabilities of the proton . 1. Virtual Compton Scattering and Generalized Polarizabilities
Virtual Compton Scattering (VCS), namely the reaction '"(p ~ n, can be understood as lepton scattering off the target which is placed in the quasi-constant electromagnetic field of the outgoing, low-energetic photon. Analogously to the form factors for elastic scattering, which describe the charge and magnetization distributions, the VCS amplitude gives access to the deformation of these distributions under the influence of the electromagnetic field. The attributed observables are called Generalized Polarizabilities GP i(Q2) [1-3], which are a natural generalization of the electric and magnetic polarizabilities accessible in Real Compton Scattering, where the four-momentum transfer squared , Q2, is O. The polarizability effect, denoted as Non-Born amplitude (cf. fig. 1), is only a small contribution to photon electro-production. The dominating contributions are the brems0375-9474/00/$ see front matter © 2000 Elsevier Science B.Y. All rights reserved. PH S0375-9474(99)00624-7
1M Friedrich et af./ Nuclear Physics A663&664 (2000) 389c-392c
390c
Bettie-HellIer
Born
Non-Born
Figure 1. The 3 processes oflowest order in photon electro-production. For clarity, crossed processes are omitted. VCS refers to both the Born and Non-Born contributions.
strahlung process on the electron (Bethe-Heitler amplitude) and on the proton (Born amplitude); they are calculable in QED, once the proton form factors for the relevant Q2 are known. We denote these contributions by BH+B. The Non-Born amplitude is obtained by subtracting the known BH+B part from the measured cross section:
d5aexp
-
dSa BH+B
= (M o - M~H+B)
+ {M l
Here, q is the momentum of the real photon
i
-
MfH +B)q' + ....
r in the proton-photon-CM-system and
0.7.------------------rn 0.6 q' = 33.6 MeV • 0.5
c. 0.4
"-'
0.1
0.09 0.08
0.07
preliminary
0.06 VCS.MAMI 0.05 ........... -175 -150 -125 -100 -75 L...L...L~-L...W
(1=0.33 G~
e=0.62
9'=O~
._...L............................................:..........................__L...L_.........'__'_'_........................................
-50
(1)
-25
0
25
eyy (deg)
Figure 2. Absolute cross sections for the investigated reaction ep -t eJYY. The known part of the cross section, d5a BH+B, is presented by the curves. The data experimental points d5a exp deviate from the curves as q' increases - the effect of the proton polarizability.
J.M. Friedrich et al./Nuclear Physics A663&664 (2000) 389c-392c
391c
is the phase space factor. The first-order term has the decomposition [3J
(2) where PLL , PIT and PL T are structure functions related to the GPi , and kinematical factors.
VLL, VLT
are
2. Measurement of Absolute Coincidence Cross Sections The absolute cross sections d5 (J ex p have been measured with the Three-SpectrometerSetup of the Al-collaboration at MAMI, where the scattered electron was measured in coincidence with the recoiling proton in two of the high-resolution spectrometers. The photon production process is selected by a cut on the missing mass around zero. From the 5 independent kinematical variables, 3 were taken to be fixed, namely the momentum transfer, q=(600±20) MeV[c, the out-of-plane angle ¢>=oo±22° (both variables taken in the proton-photon-CM-system), and the virtual photon polarization f=O.62±O.02 (the ranges are given by the acceptances of the spectrometers). In each group, the wide range of iJ~~{ from -152° to +17° was covered by only changing the setting of the proton spectrometer. This angular range covers the backward direction relative to the incoming and outgoing electrons. Here, the proton contributions are dominant, since the bremsstrahlung is emitted predominantly in the electron directions.
1: ~
C '-'
...
10 7.5
.t C'
5
~ IIlc
2.5
Pu.- PTT/t:=30.2
± 2.2 -620
~
~
i
-51" -39·
•
-9 •
-
tT
1"
-17"
;- -129 ~-141 -118" 0
-28·
0
rt,r
4
PLT=-8.8 ± 0.8 t/12=2.2
-2.5 -5 -7.5
-90·
t -12.5
,fl< O·
-15 -0.1
0
0.1
~ -.I
0.2
0.3
01'
-150·
0.4
0.5
vLL!VL T
Figure 3. Compilation of the complete data set (statistical errors only) according to eq. (2) and assuming no evolution in q' (cf. eq. (1)). This allows to extract two combinations of the structure functions by linear regression, with statistical errors and the X2 given.
392c
JM Friedrich et al. /Nuclear Physics A 663&664 (2000) 389c-392c
The reliability of the experimental data is tested in kinematical overlaps of different settings. Settings were taken overlapping in iJ~"IM for every q'; the cross sections are found to agree within the statistical accuracy. Another consistency test between the different q'-settings has the same result. Radiative corrections have been applied to the experimental data. All contributing diagrams that do not depend on the cutoff in the missing mass have been evaluated in leading order [4]. For soft photon emission, which causes a radiative tail in the missing mass spectrum, a correction factor has been applied, that was taken equivalently to the correction in the elastic case. The error of this approximation is still under investigation.
3. Results From the measured cross sections we extract the two combinations of structure functions in eq. (2) as shown in fig. 2. The result is compared in Table 1 with theoretical predictions, showing best agreement with Heavy Baryon Chiral Perturbation Theory. Table 1 Results and theoretical predictions. The errors on the experimental values include also systematic errors. PLL
preliminary This Experiment
HBChPT LSM ELM NRCQM
-
PTT/f. [GeV- 2 ]
P LT [GeV- 2 ]
30.2 ± 6
-8.8 ± 4
26.3
-5.7
10.9 5.9 17.0
0 -1.9 -1.7
HBChPT: Heavy Baryon Chiral Perturbation Theory [5] LSM: Linear Sigma Model [6] ELM: Effective Lagrangian Model [7] NRCQM: Non-Relativistic Constituent Quark Model [8]
REFERENCES 1. P.A.M. Guichon et al, Nuc. Phys. A 591, 606 (1995) 2. D. Drechsel et al, Phys. Rev. C 55, 424 (1997) and Phys. Rev. C 57, 941 (1998) 3. P.A.M. Guichon et M. Vanderhaeghen, Prog. 41, 125 (1998) 4. M. Vanderhaeghen et al, to be published 5. T.R. Hemmert, B.R. Holstein, G. Knoehlein and S. Scherer, Phys. Rev. D 55, 2630 (1997) and Phys. Rev. Lett. 79, 22 (1997) 6. A. Metz and D. Drechsel, Z. Phys. A 359, 165 (1997) and Z. Phys. A 356, 351 (1996) 7. M. Vanderhaeghen, Phys. Lett. B 368, 13 (1996) 8. G.Q. Liu, A.W. Thomas, P.A.M. Guichon, Aust. J. Phys. 49, 905 (1996)
ELSEVIER
_A Nuclear Physics A663&664 (2000) 389c-392c www.elsevier.nl/locatelnpe
The First Dedicated Virtual Compton Scattering Experiment at MAMI J. M. Friedrich", P. Bartsch", D. Baumann", J. Berthot" , P. Y. Bertin", V. Breton" , W. U. Boeglin", R. Bohma , N. d'Hose", T. Caprano" , S. Derber", N. Degrande", M. Ding" , M. O. Distler", J. E. Ducret", R. EdelhofP, 1. Ewalda , H. Fonvieille'' , J. Friedrich", R. Geiges", Th . Gousset", P. A. M. Ouichon" , H. HolvoetC , Ch. Hyde-Wright", P. Jennewein", M. Kahrau", S. Kerhoas", M. Korn", H. Kramer", K. W. Krygier", V. Kunde", B. Lannoy", D. Lhuillier", A. Liesenfeld", C. Marchand", D. Marchand", J. Martino", H. Merkel", K. Merle", P. Merle", G. De Meyer", J. Mougey", R. Neuhausen", E. Offermann", Th. Pospischil", G. Quemener", O. Raveld , Y. Roblin", J. Roche", D. Rohe", G. Rosner", D. Ryckbosch", P. Sauer", H. Schmieden", S. Schardt" , G. Tamas", M. Tytgat" , M. Vanderhaeghen" , L. Van Hoorebeke", R. Van de VyverC , J. Van de Wielef , P. Vernia", A. Wagner", Th . Walcher" "Inst itut fur Kernphysik, Universitat Mainz, Germany bDAPNIAjSPhN, CEAjSaclay, F91191 Gif-sur-Yvette Cedex, France cUniversity of Gent , Belgium dLPC, Universite Blaise Pascal, IN2P3jCNRS Aubiere, France "Old Dominion University, Virginia, USA fIPN , IN2P3 Orsay, France We measured the absolute cross sections for photon electro-production off the prot on, ep ~ en, with the high resolution spectrometers at MAMI at momentum transfer q = 600 MeVjc and photon polarization (': = 0.62. We covered the momentum range for the outgoing real photon q' = 33-:-111 MeVjc. From the extr acted Virtual Compton Scattering amplitude we deduce values for two structure functions related to the generalized polarizabilities of the proton . 1. Virtual Compton Scattering and Generalized Polarizabilities
Virtual Compton Scattering (VCS), namely the reaction '"(p ~ n, can be understood as lepton scattering off the target which is placed in the quasi-constant electromagnetic field of the outgoing, low-energetic photon. Analogously to the form factors for elastic scattering, which describe the charge and magnetization distributions, the VCS amplitude gives access to the deformation of these distributions under the influence of the electromagnetic field. The attributed observables are called Generalized Polarizabilities GP i(Q2) [1-3], which are a natural generalization of the electric and magnetic polarizabilities accessible in Real Compton Scattering, where the four-momentum transfer squared , Q2, is O. The polarizability effect, denoted as Non-Born amplitude (cf. fig. 1), is only a small contribution to photon electro-production. The dominating contributions are the brems0375-9474/00/$ see front matter © 2000 Elsevier Science B.Y. All rights reserved. PH S0375-9474(99)00624-7
1M Friedrich et af./ Nuclear Physics A663&664 (2000) 389c-392c
390c
Bettie-HellIer
Born
Non-Born
Figure 1. The 3 processes oflowest order in photon electro-production. For clarity, crossed processes are omitted. VCS refers to both the Born and Non-Born contributions.
strahlung process on the electron (Bethe-Heitler amplitude) and on the proton (Born amplitude); they are calculable in QED, once the proton form factors for the relevant Q2 are known. We denote these contributions by BH+B. The Non-Born amplitude is obtained by subtracting the known BH+B part from the measured cross section:
d5aexp
-
dSa BH+B
= (M o - M~H+B)
+ {M l
Here, q is the momentum of the real photon
i
-
MfH +B)q' + ....
r in the proton-photon-CM-system and
0.7.------------------rn 0.6 q' = 33.6 MeV • 0.5
c. 0.4
"-'
0.1
0.09 0.08
0.07
preliminary
0.06 VCS.MAMI 0.05 ........... -175 -150 -125 -100 -75 L...L...L~-L...W
(1=0.33 G~
e=0.62
9'=O~
._...L............................................:..........................__L...L_.........'__'_'_........................................
-50
(1)
-25
0
25
eyy (deg)
Figure 2. Absolute cross sections for the investigated reaction ep -t eJYY. The known part of the cross section, d5a BH+B, is presented by the curves. The data experimental points d5a exp deviate from the curves as q' increases - the effect of the proton polarizability.
J.M. Friedrich et al./Nuclear Physics A663&664 (2000) 389c-392c
391c
is the phase space factor. The first-order term has the decomposition [3J
(2) where PLL , PIT and PL T are structure functions related to the GPi , and kinematical factors.
VLL, VLT
are
2. Measurement of Absolute Coincidence Cross Sections The absolute cross sections d5 (J ex p have been measured with the Three-SpectrometerSetup of the Al-collaboration at MAMI, where the scattered electron was measured in coincidence with the recoiling proton in two of the high-resolution spectrometers. The photon production process is selected by a cut on the missing mass around zero. From the 5 independent kinematical variables, 3 were taken to be fixed, namely the momentum transfer, q=(600±20) MeV[c, the out-of-plane angle ¢>=oo±22° (both variables taken in the proton-photon-CM-system), and the virtual photon polarization f=O.62±O.02 (the ranges are given by the acceptances of the spectrometers). In each group, the wide range of iJ~~{ from -152° to +17° was covered by only changing the setting of the proton spectrometer. This angular range covers the backward direction relative to the incoming and outgoing electrons. Here, the proton contributions are dominant, since the bremsstrahlung is emitted predominantly in the electron directions.
1: ~
C '-'
...
10 7.5
.t C'
5
~ IIlc
2.5
Pu.- PTT/t:=30.2
± 2.2 -620
~
~
i
-51" -39·
•
-9 •
-
tT
1"
-17"
;- -129 ~-141 -118" 0
-28·
0
rt,r
4
PLT=-8.8 ± 0.8 t/12=2.2
-2.5 -5 -7.5
-90·
t -12.5
,fl< O·
-15 -0.1
0
0.1
~ -.I
0.2
0.3
01'
-150·
0.4
0.5
vLL!VL T
Figure 3. Compilation of the complete data set (statistical errors only) according to eq. (2) and assuming no evolution in q' (cf. eq. (1)). This allows to extract two combinations of the structure functions by linear regression, with statistical errors and the X2 given.
392c
JM Friedrich et al. /Nuclear Physics A 663&664 (2000) 389c-392c
The reliability of the experimental data is tested in kinematical overlaps of different settings. Settings were taken overlapping in iJ~"IM for every q'; the cross sections are found to agree within the statistical accuracy. Another consistency test between the different q'-settings has the same result. Radiative corrections have been applied to the experimental data. All contributing diagrams that do not depend on the cutoff in the missing mass have been evaluated in leading order [4]. For soft photon emission, which causes a radiative tail in the missing mass spectrum, a correction factor has been applied, that was taken equivalently to the correction in the elastic case. The error of this approximation is still under investigation.
3. Results From the measured cross sections we extract the two combinations of structure functions in eq. (2) as shown in fig. 2. The result is compared in Table 1 with theoretical predictions, showing best agreement with Heavy Baryon Chiral Perturbation Theory. Table 1 Results and theoretical predictions. The errors on the experimental values include also systematic errors. PLL
preliminary This Experiment
HBChPT LSM ELM NRCQM
-
PTT/f. [GeV- 2 ]
P LT [GeV- 2 ]
30.2 ± 6
-8.8 ± 4
26.3
-5.7
10.9 5.9 17.0
0 -1.9 -1.7
HBChPT: Heavy Baryon Chiral Perturbation Theory [5] LSM: Linear Sigma Model [6] ELM: Effective Lagrangian Model [7] NRCQM: Non-Relativistic Constituent Quark Model [8]
REFERENCES 1. P.A.M. Guichon et al, Nuc. Phys. A 591, 606 (1995) 2. D. Drechsel et al, Phys. Rev. C 55, 424 (1997) and Phys. Rev. C 57, 941 (1998) 3. P.A.M. Guichon et M. Vanderhaeghen, Prog. 41, 125 (1998) 4. M. Vanderhaeghen et al, to be published 5. T.R. Hemmert, B.R. Holstein, G. Knoehlein and S. Scherer, Phys. Rev. D 55, 2630 (1997) and Phys. Rev. Lett. 79, 22 (1997) 6. A. Metz and D. Drechsel, Z. Phys. A 359, 165 (1997) and Z. Phys. A 356, 351 (1996) 7. M. Vanderhaeghen, Phys. Lett. B 368, 13 (1996) 8. G.Q. Liu, A.W. Thomas, P.A.M. Guichon, Aust. J. Phys. 49, 905 (1996)